Machine design involves selecting and sizing components to transmit motion and force safely. A keyway is a slot machined into a shaft and hub to receive a key that transmits torque between them. A flywheel stores rotational kinetic energy to smooth out fluctuations in angular velocity during a machine cycle. The gear ratio \(GR = N_2/N_1 = \omega_1/\omega_2\) determines how rotational speed and torque are traded between meshing gears. Bearings reduce friction and support loads between moving parts; journal bearings rely on a fluid film of sliding contact, while rolling-element bearings use balls or rollers to minimize friction.
Springs are characterized by a stiffness \(k = F/\delta\). When springs combine in series, the equivalent stiffness obeys \(1/k_{eq} = 1/k_1 + 1/k_2 + \ldots\) and is softer than any individual spring, while in parallel the equivalent stiffness is \(k_{eq} = k_1 + k_2 + \ldots\) and is stiffer than any individual spring. The critical speed of a shaft is the rotational speed at which its natural frequency of vibration matches the operating speed, leading to dangerous resonance. Power screws convert rotary motion into linear motion and are used in jacks and presses. The mechanical advantage of a lever, \(MA = F_{out}/F_{in} = d_{in}/d_{out}\), relates output force to the ratio of lever arm distances.
Rotational quantities play a central role: torque \(T = F \times r\) is the rotational equivalent of force, and power is related to torque and angular velocity by \(P = T\omega\). Two key formulas govern the stress state in common machine elements. The torsion formula \(\tau = Tr/J\) gives the shear stress in a circular shaft, where \(J\) is the polar moment of inertia. The flexure formula \(\sigma = My/I\) gives the bending stress in a beam, where \(M\) is the bending moment, \(y\) is the distance from the neutral axis, and \(I\) is the moment of inertia of the cross-section.
Manufacturing processes shape raw materials into finished parts. Casting pours molten metal into a mold to solidify into the desired shape. Forging shapes metal using compressive forces, refining its grain structure. Hot working is performed above the recrystallization temperature, while cold working is done below it and increases hardness through strain hardening. Turning on a lathe rotates a workpiece against a stationary cutting tool to produce cylindrical shapes, while milling uses a rotating multi-point cutter to remove material from a stationary workpiece. Welding joins materials by applying heat, pressure, or both. MIG (GMAW) uses a consumable wire electrode and is faster, while TIG (GTAW) uses a non-consumable tungsten electrode for higher precision. Powder metallurgy compacts metal powder in a die and sinters it below the melting point, while injection molding forces molten plastic into a mold cavity under high pressure.
Material selection depends on the required properties. Hardness measures resistance to localized plastic deformation (indentation or scratching) and is commonly measured by Brinell, Rockwell, or Vickers tests. Brittle fracture occurs suddenly with little plastic deformation, whereas ductile fracture involves substantial plastic deformation before breaking. An alloy is a mixture of two or more elements, at least one a metal, designed to achieve improved mechanical or chemical properties, and ferrous metals are those in which iron is the primary element, such as steel and cast iron.
Finally, all mechanical engineering calculations rely on a consistent set of units. The SI system defines the Newton (N) as the unit of force (1 kg·m/s²), the Pascal (Pa) as the unit of pressure (1 N/m²), the Joule (J) as the unit of energy and work (1 N·m), and the Watt (W) as the unit of power (1 J/s). Common conversions include 1 bar = 100,000 Pa, 1 N ≈ 0.2248 lbf, 1 hp ≈ 745.7 W, 1 atm = 101,325 Pa, 1 BTU ≈ 1055.06 J, and the temperature shift \(K = °C + 273.15\).